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Invariants for Homology 3-Spheres

  • Nikolai┬áSaveliev

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 140)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Nikolai Saveliev
    Pages 1-34
  3. Nikolai Saveliev
    Pages 35-49
  4. Nikolai Saveliev
    Pages 51-85
  5. Nikolai Saveliev
    Pages 87-98
  6. Nikolai Saveliev
    Pages 99-121
  7. Nikolai Saveliev
    Pages 123-183
  8. Nikolai Saveliev
    Pages 185-203
  9. Back Matter
    Pages 205-223

About this book

Introduction

Homology 3-sphere is a closed 3-dimensional manifold whose homology equals that of the 3-sphere. These objects may look rather special but they have played an outstanding role in geometric topology for the past fifty years. The book gives a systematic exposition of diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered in the book are constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its numerous extensions, including invariants of Walker and Lescop, Herald and Lin invariants of knots, and equivariant Casson invariants, followed by Floer homology and gauge-theoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. It will be appealing to both graduate students and researchers in mathematics and theoretical physics.

Keywords

Algebraic topology Casson invariant Euler characteristic Floer homology Gauge theory Homotopy Invariants of knots and 3-- manifolds Rokhlin invariant Theoretical physics algebra homology homology cobordism homomorphism

Authors and affiliations

  • Nikolai┬áSaveliev
    • 1
  1. 1.Department of MathematicsUniversity of MiamiCoral GablesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04705-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07849-1
  • Online ISBN 978-3-662-04705-7
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site